The study area is located in the eastern part of the Nile Delta Figure 1.

Landsat 8 image on Jul. 26th, 2016, (path 192/row 030) around 10 a.m. local time with 30 meter ground resolution and Sentinel-1 radar data on Jul. 26th, 2016 with 10 meter ground resolution were used.

Landsat 8 bands 4 and 5 provide red (R) and near-infra red (NIR) measurements and therefore can be used to generate NDVI with the following formula:

NDVI = (Band 5 − Band 4)/(Band 5 + Band 4) (1)

The recorded Digital Numbers (DN) were converted to radiance units (Rad) using the calibration coefficients specific for each band. Band 10 was used to extract LST as follows:

Rad = 0.0003342 * DN + 0.10000 (2)

Surface emissivity (Eo) was estimated from NDVI using the empirical equation developed from raw data on NDVI and thermal emissivity [19].

Eo = 0.9932 + 0.0194 lnNDVI (3)

The radiant temperature (To) can be calculated from band 10 radiance (Rad 10) using calibration constants K1 = 774.89 and K2 = 1321.08.

To = K2/ln((K1/Rad10) + 1) (4)

The resulting temperature (Kelvin) is the satellite radiant temperature of the

viewed earth atmosphere system, which is correlated with, but not the same as, the surface (kinetic) temperature. The atmospheric effects and surface thermal

emissivity have to be considered in order to obtain an accurate estimate of surface temperature from satellite thermal data [20]. LST is calculated from the top of atmosphere radiant temperature (To) and estimated surface emissivity (Eo) as:

LST = To/Eo (5)

[15] showed that there is a unique mathematical relationship between CWSI and evapotranspiration from vegetation surface as follows:

where ETa is the actual evapotranspiration, ETc is the potential crop evapotranspiration and CWSI is Crop Water Stress Index. CWSI approach was preceded and developed by [14] [15]. They proposed the empirical and theoretical methods to estimate CWSI as follows:

Where: ∆T is the difference between measured surface and air temperature, ∆Tm is the difference between minimum surface and air temperature and ∆Tx is the difference between maximum surface and air temperature. Since all variables have the same units, CWSI is a dimensionless ratio. The lower limit of dT occurs under non-water-stressed conditions when ET is only limited by atmospheric demand. On the other hand, the upper limit of dT is reached under non-trans- piring conditions when ET is stopped due to the lack of water. The values of CWSI are ranged between zero and one where zero indicates no stress and value of one indicates maximum stress.

Many researchers studied the relationship between Kc and NDVI. Similarities between Kc curve and a satellite-derived vegetation index showed potential for modeling a Kc as a function of the vegetation index [21]. Therefore, the possibility of directly estimating Kc from satellite data was investigated [5] and [22] [23].[5] represented the relation between Kc and NDVI through Equation (8) which calibrated for wheat by [23].

where; 1.2 is the maximum Kc, NDVI_dv is the difference between minimum and maximum NDVI value for vegetation and NDVI_mv is the minimum NDVI value for vegetation.

ETo was calculated from meteorological data using the FPM method (Equation (9)) which was derived by [24]. This formula was applied to calculate ETo.

Where; ETo, reference evapotranspiration [mm/day], R_n, net radiation at the crop surface [MJ/m²/day], G, soil heat flux density [MJ/m²/day], T, mean daily air temperature at 2 m height [˚C], u₂, wind speed at 2 m height [m/s], e_s, saturation vapour pressure [kPa], e_a, actual vapour pressure [kPa], e_s − e_a, saturation vapour pressure deficit [kPa], Δ, slope vapour pressure curve [kPa/˚C], γ, psychrometric constant [kPa/˚C].

Equations (8) and (9) were used to estimate (ETc) as shown in equation (10).

ETc = ETo * Kc (10)

The crop and soil water content are indexed by the calibrated radar data of the backscattered VV-polarization data. According to SNAP software help manual, the objective of SAR calibration is to provide imagery in which the pixel values can be directly related to the radar backscatter of the scene. To do this, the application output scaling applied by the processor must be undone and the desired scaling must be applied. Level-1 products provide four calibrations Look Up Tables (LUTs) to produce β0i, σ0i and γi or to return to the DN. The LUTs apply a range-dependent gain including the absolute calibration constant. For Ground Range Detected (GRD) products, a constant offset is also applied.

The radiometric calibration is applied by the following equation:

where, depending on the selected LUT,

= one of, or

= one of, and or

The bi-linear interpolation is used for any pixels that fall between points in the LUT.

ETc was estimated through Equation (10) based on two parameters which are ETo and Kc. [3] and [25] [26] used the FPM method, to estimate ETo based on ground meteorological data to evaluate or to couple with the remotely sensed data. ETo was estimated from ground meteorological data according to the FPM model. ETo value was 6.7 mm/day.

Many researchers studied the relation between Kc and NDVI [27] [28] [29] [30]. They demonstrated that ET for irrigated agriculture can be estimated by applying empirical data to develop a relationship between the NDVI and Kc. [31] [32] similarly used remote sensing to estimate Kcb. They found that Kcb methods can be transformed to Kc methods by adding an estimate for Ke to Kcb.

The relation between Kc and NDVI is highly correlated where both of them are varying from planting to senescence in the same way. NDVI is calculated from Red and NIR bands, and varying according to crop age, planting density and chlorophyll activity. The results of Kc values varied from 0 to 1.2.

In the study area, ETc values varied from 0 to 7.8 mm/day according to land cover type, crop stage and weather conditions as shown in Figure 2.

In arid and semi-arid climates, ET ranges over a large interval depending on water regimes. Moreover, the variation in one weather parameter immediately influences all the other variables that are mutually related. This fact makes it difficult to correctly evaluate the ETa [33]. [34] analyzed the efficiency of three methods based on the FAO-56 Kc approach to estimate ETa for winter wheat under different irrigation treatments under the semi-arid conditions of Morocco. ETa was estimated according to Equation (6). It was affected by the changes in CWSI and ETc. The values of ETa varied from 0 to 6.4 mm/day. As shown as in Figure 2, the increasing in ETa was observed according to land cover type, crop stage, weather conditions and water stress conditions.

The radar data from the European Space Agency’s Sentinel-1A/B Ground Range Detected High Resolution (GRDHR), was used after radiometric and geometric calibration to represent the SAR data. On the other hand, the Landsat 8 data was used to calculate NDVI, LST, CWSI and ETa.

The backscattering data increased according to crop and soil water content. According to Figure 3, the relation between backscattering and NDVI was good and R² was as high as 0.9, while the relation between backscattering and LST was an inverse relationship and R² was as high as 0.82. The relation between the backscattering and CWSI was an inverse relationship and R² was 0.82. On the other hand the relationship between the backscattering and ETa was logarithmic with a high R² (0.88).